shitthink is defined by people who just shit out their thoughts or words without actually thinking or by deliberately being willfully stupid and expressing themselves.
More often than not shitthink is characterized by a close affiliation to right wing hate groups, but they often also are connected to just right wing groups as well.
Shitthink is also many times mere right wing dogma and/or policies.

1. The church spewed out more shitthink.

2. That was typical, stupid, redneck shitthink!

3. Sarah Palin only uses shitthink in public and likely in private too.